Light hadron spectroscopy using domain wall valence quarks on an Asqtad sea

TL;DR

The paper presents a comprehensive lattice QCD study of the light hadron spectrum using domain-wall valence quarks on a 2+1 flavor Asqtad sea. It reports meson and baryon spectra, decay constants, and extensive chiral extrapolations using both SU(2) and SU(3) heavy-baryon chiral perturbation theory, including mixed-action EFT. A key finding is the nucleon mass exhibiting an almost linear dependence on the pion mass across the explored range, a behavior also seen in other groups, which challenges standard chiral extrapolations and underscores convergence issues in SU(3) HB$\chi$PT and the need for multiple lattice spacings, volumes, and observables to constrain low-energy constants. The results show improved baryon masses relative to coarse MILC lattices, but reveal significant uncertainties in axial couplings and chiral convergence, highlighting the importance of further simulations at lighter masses and with more volumes to draw definitive conclusions about QCD baryon structure.

Abstract

We calculate the light hadron spectrum in full QCD using two plus one flavor Asqtad sea quarks and domain wall valence quarks. Meson and baryon masses are calculated on a lattice of spatial size $L \approx 2.5$\texttt{fm}, and a lattice spacing of $a \approx 0.124$\texttt{fm}, for pion masses as light as $m_π\approx 300$\texttt{MeV}, and compared with the results by the MILC collaboration with Asqtad valence quarks at the same lattice spacing. Two- and three-flavor chiral extrapolations of the baryon masses are performed using both continuum and mixed-action heavy baryon chiral perturbation theory. Both the three-flavor and two-flavor functional forms describe our lattice results, although the low-energy constants from the next-to-leading order SU(3) fits are inconsistent with their phenomenological values. Next-to-next-to-leading order SU(2) continuum formulae provide a good fit to the data and yield and extrapolated nucleon mass consistent with experiment, but the convergence pattern indicates that even our lightest pion mass may be at the upper end of the chiral regime. Surprisingly, our nucleon masses are essentially lineaer in $m_π$ over our full range of pion masses, and we show this feature is common to all recent dynamical calculations of the nucleon mass. The origin of this linearity is not presently understood, and lighter pion masses and increased control of systematic errors will be needed to resolve this puzzling behavior.

Figures (17)

• Figure 1: The left-hand figure shows the residual mass determined from the ratio $R(t)$ in Eq. (\ref{['eq:rt']}), for the data at $a m_{u/d}^{\rm asqtad} = 0.010$; the quoted value of $m_{\rm res}$ is obtained from a constant fit to the data. Note that the effect of the Dirichlet boundary at $t = 22$ relative to the source is apparent as far out as $t = 14$. The right-hand figure shows the quark-mass dependence of the residual mass. The main reason for the increase in $m_{\rm res}$ with decreasing $a m_{u/d}^{\rm asqtad}$ is the increased roughening of the gauge field; in typical quenched calculations, a smaller dependence of the residual mass on the quark mass is observed. As a result, chiral symmetry is satisfied to a lesser degree at fixed $L_s$ as the pion mass decreases.
• Figure 2: The pion (left) and kaon (right) effective masses at each value of the light-quark mass, together with the single-exponential fits to the correlators, as described in the text. The oscillatory terms in the transfer matrix are evident in the effective mass close to the source.
• Figure 3: Comparison between pseudo-scalar and vector masses with domain wall valence quarks (LHP) and staggered valence quarks (MILC) computed on the coarse ($a\approx 0.125$fm) MILC ensembles.
• Figure 4: Two types of "bubble" contributions to the scalar meson: the left one is $B_1$ in Eq. (\ref{['eq:a0-bubble']}) while the right panel is $B_2$ in Eq. (\ref{['eq:a0-bubble']}).
• Figure 5: The left panel of this figure shows the "effective" point-point scalar meson correlator plot (as defined in Eq. (\ref{['eq:C_PP-eff']})), along with the mixed-action bubble contribution from Eq. (\ref{['eq:a0-bubble']}). Note that the symbols are the same as in Fig. \ref{['fig:PS-meson']}. The right hand panel shows the fits to data from the lightest three ensembles where the largest "bubble" contributions dominate.